Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
120 conjugacy classes of subgroups; only the 23 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 23 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #20260528 | C2 | semidirect |
| 3. #353×C97 | C2 | semidirect |
| 6. #15690807 | C4 | semidirect |
| 8. C4×#11715895 | C4 | semidirect |
| 53. C97 | #1408 | semidirect |
| 56. #353 | D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261111 | 2 |
| #20260528 | 2 |
| #353×C97 | 2 |
| #1408 | 97 |